Preheat the oven to 350°F (175°C).

Smear 1 tablespoon butter all over the inside of a 10-cup (2.5-liter) Bundt cake or tube pan. Sprinkle the 2 teaspoons of rosemary evenly into the pan, then dust with the 2 tablespoons (20 g) of polenta, tilting the pan to coat the sides.

To make the cake, in a small bowl, sift together the flour, ¾ cup (130 g) polenta, baking powder, and salt. Set aside. In a separate bowl, whisk the olive oil, eggs, egg yolks, and almond or vanilla extract.

In a stand mixer fitted with the paddle attachment (or in a bowl by hand), beat together ½ cup (4 ounces/115 g) butter and the sugar on medium speed until light and fluffy, 3 to 5 minutes. With the mixer running, slowly dribble in the egg mixture, a little at a time, until completely incorporated. Stir in the flour mixture along with the 4 teaspoons of rosemary until just incorporated. Don't over mix.

Scrape the batter into the prepared cake pan and smooth the top. Bake until a toothpick inserted into the center comes out clean, about 40 minutes. Let cool for about 30 minutes, then invert the cake onto a serving plate.

Storage: The cake will keep at room temperature for up to 4 days, well wrapped. It can be frozen for up to 2 months.